This article provides a mathematical description of the working process of a promising gas seal, which operates with performance characteristics similar to those of the latest gas-dynamic seals but uses a completely different principle of creating the gas barrier, preventing leakage of the pumped product from the pump at the outlet its rotating rotor from the casing. The proposed mathematical dependencies make it possible to calculate the geometric parameters of the sealing rings, which are the main working components of the seal, and to determine the static and dynamic characteristics of the working process in the seal.